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Bifurcations at Infinity in General 3D Piecewise-Smooth Quadratic Vector Fields.

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Title: Bifurcations at Infinity in General 3D Piecewise-Smooth Quadratic Vector Fields.
Authors: Huang, Xiezhen1,2 (AUTHOR) 270923365@qq.com, Feng, Chunsheng3 (AUTHOR) spring@xtu.edu.cn, Liu, Yongjian2 (AUTHOR) liuyongjianmaths@126.com
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Feb2026, Vol. 36 Issue 2, p1-25. 25p.
Subjects: Bifurcation theory, Infinity (Mathematics), Nonlinear mechanics, Smoothness of functions, Vector fields, Poincare maps (Mathematics)
Abstract: This paper investigates bifurcations at infinity, in general, Three-Dimensional (3D) piecewise-smooth quadratic vector fields. We derive the expression for the sliding vector field in the switching region at infinity utilizing the Poincaré compactification and the Filippov convention. Then, we establish the parameter conditions under which the piecewise smooth system exhibits local codimension-0 singularities, regular points on the discontinuity boundary, and codimension-1 singularities at infinity. These findings offer valuable insights into the complex dynamics of piecewise smooth nonlinear vector fields. Finally, the main results are applied to two models of 3D variable-boostable chaotic flows, whose vector fields contain only square (e.g. x 2 , y 2 and z 2 ) or cross-product terms (e.g. x y , y z and z x), and the phase portraits of the dynamic behaviors at infinity are described. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 190698713
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  Data: Bifurcations at Infinity in General 3D Piecewise-Smooth Quadratic Vector Fields.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Feb2026, Vol. 36 Issue 2, p1-25. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Infinity+%28Mathematics%29%22">Infinity (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+mechanics%22">Nonlinear mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Smoothness+of+functions%22">Smoothness of functions</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink><br /><searchLink fieldCode="DE" term="%22Poincare+maps+%28Mathematics%29%22">Poincare maps (Mathematics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper investigates bifurcations at infinity, in general, Three-Dimensional (3D) piecewise-smooth quadratic vector fields. We derive the expression for the sliding vector field in the switching region at infinity utilizing the Poincaré compactification and the Filippov convention. Then, we establish the parameter conditions under which the piecewise smooth system exhibits local codimension-0 singularities, regular points on the discontinuity boundary, and codimension-1 singularities at infinity. These findings offer valuable insights into the complex dynamics of piecewise smooth nonlinear vector fields. Finally, the main results are applied to two models of 3D variable-boostable chaotic flows, whose vector fields contain only square (e.g. x 2 , y 2 and z 2 ) or cross-product terms (e.g. x y , y z and z x), and the phase portraits of the dynamic behaviors at infinity are described. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S021812742650015X
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 25
        StartPage: 1
    Subjects:
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Infinity (Mathematics)
        Type: general
      – SubjectFull: Nonlinear mechanics
        Type: general
      – SubjectFull: Smoothness of functions
        Type: general
      – SubjectFull: Vector fields
        Type: general
      – SubjectFull: Poincare maps (Mathematics)
        Type: general
    Titles:
      – TitleFull: Bifurcations at Infinity in General 3D Piecewise-Smooth Quadratic Vector Fields.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Huang, Xiezhen
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          Name:
            NameFull: Feng, Chunsheng
      – PersonEntity:
          Name:
            NameFull: Liu, Yongjian
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          Dates:
            – D: 01
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
          Identifiers:
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              Value: 02181274
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              Value: 36
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              Value: 2
          Titles:
            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
              Type: main
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